Influence of Conjugacy Class sizes on Sylow Subgroups

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• Julian Brough Cambridge University
• Friday 25 October 2013, 15:00-16:00
• CMS, MR5.

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Given a group G and x in G, the size of the conjugacy class of x in G is given by the size of the group divided by the order. This number will be refered to as the index of x. In the subject of representation theory, conjugacy class sizes form a key component in the construction of the character table of a group, for example in the orthogonality relations. The character table then enables us to determine group structures such as normal subgroups or see how conjugacy classes multiply together. Hence it is natural to ask what other properties can be determined by conjugacy class sizes.

This talk is part of the Junior Algebra and Number Theory seminar series.

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